POP Steering parameterization

Eddy diffusivity implementation by Bates, Tulloch, Marshall, and Ferrari

Steering Sensitivity Experiments 023,024,025 (alpha,b1,gamma)

This is a suite of sensitivity experiments testing the sensitivity of alpha, gamma and b1.

Experiment 23:

alpha = 8; gamma = 0.8; b1 = 4
/glade/u/home/jet/cases/g.e11.GIAF.T62_gx1v6.steer.023

Experiment 24:

alpha = 8; gamma = 0.8; b1 = 1
/glade/u/home/jet/cases/g.e11.GIAF.T62_gx1v6.steer.024

Experiment 25:

alpha = 8; gamma = 0.35; b1 = 1
/glade/u/home/jet/cases/g.e11.GIAF.T62_gx1v6.steer.025

Notes:

  • In our simulations, we use gamma = 1.75. If we stick with the definition of gamma given in the Appendix of Bates et al. (2014), gamma represents mixing efficiency and cannot exceed 1. However, we can interpret it as const * gamma where we have introduced a scaling constant (const).

  • There is also some very sensitive relationship between b1 and gamma as shown in the paragraph just below A6b.

Comparison of Relavant fields

The fields which are affected by alpha, b1 and gamma are:

  • \(u_{rms} = alpha*{\sigma_{vi}}*L_{eddy}\)

  • \(u_{rms}^2\)

  • \({(U-c)}^2 \over {u_{rms}^2}\)

  • \({Suppression \quad factor = {1 \over (1 + b1 * |\bar u - c|^2 /u_{rms (z=0)}^2 )}}\)

  • \({K}=u_{rms}∗{\Gamma * L_{eddy} \over (1 + b1 * |u_{mean} - c|^2 /u_{rms}^2 (z=0)}\)


\(\color{green}{Comparing \quad RMS \quad eddy \quad velocity}\quad \color{red}{u_{rms}}\)


NOTES:

Alpha was changed to 8.0 for all three sensitivity experiments. It will be compared to the 018 control run and Bate's et al.

  • \(u_{rms} = alpha*{\sigma_{vi}}*L_{eddy}\)

  • alpha (scaling constant) = 8
  • \(\sigma_{vi} = {f \over \sqrt{R_i}}\quad = \quad {f \over \sqrt{{f^2N^2 \over m^4}}}\quad = \quad {{\cancel f m^2} \over \cancel f N}\)

  • \(u_{rms}\) is limited to 5 cm/s $ max(u_{rms},5.)$

\(\quad\quad\quad\quad\quad\quad\quad\) Eddy Velocity \((u_{rms})\quad\) CESM

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\(\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad u_{rms} \) Bates et al

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\(\color{green}{u_{rms}^2 \quad Term} \quad\)


NOTES:

  • \(K={u_{rms}}∗{\Gamma * L_{eddy} \over (1 + b1 * |u_{mean} - c|^2 /\color{red}{u_{rms}^2} (z=0)} \)
  • \(u_{rms}^2\) is a surface value
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\(\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad u_{rms}^2 \) Bates et al

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\(\quad\quad\quad\quad\quad\quad\) \({(U-c)}^2 \over {u_{rms}^2} \quad\) CESM

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\(\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad {|u-c|^2 \over u_{rms}^2} \) Bates et al

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\(\color{green}{\quad Suppression \quad factor = {1 \over (1 + b1 * |\bar u - c|^2 /u_{rms (z=0)}^2 )}}\)


NOTES:

  • \(c = max(- \beta * L_{eddy}^2,-20)\)
  • \(u_{rms} = max(u_{rms},5.)\)
  • \(u_{rms}^2\) is a surface value
  • \(b1\) (scaling constant) = 4. (case23) , 1. (case24), or 1. (case25)

\(\quad\quad\quad\quad\quad\quad\quad\) Suppression Factor CESM

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\(\quad\quad\quad\quad\quad\quad\quad\) Suppression Factor Bates

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\(\quad\quad\quad\quad\quad\quad\quad\) Suppression Factor (Zonal x depth) CESM

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\(\quad\quad\quad\quad\quad\quad\quad\) Suppression Factor (Zonal x depth) Bates

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\(\color{green}{\quad Parameterizing \quad Eddy \quad Diffusivity \quad} (\color{red}{K})\)


NOTES:

  • \(\color{red}{K}=u_{rms}∗{\Gamma * L_{eddy} \over (1 + b1 * |u_{mean} - c|^2 /u_{rms}^2 (z=0)}\)

\(\quad\quad\quad\quad\quad\quad\quad\) Eddy Diffusivity (K) CESM

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\(\quad\quad\quad\quad\quad\quad\quad\) Eddy Diffusivity (K) Bates

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\(\quad\quad\quad\quad\quad\quad\quad\) (Zonal x Depth) CESM

\(\quad\quad\quad\quad\quad\quad\quad\quad\quad\) K limited to (100 < K < 10000)

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Here is the Bate's version

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pCFC 11 biases at year 297

GLODAP vs CESM control and New Steering Param (Exp018)

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pCFC 11 biases in sensitivity experiments 23, 24 and 25

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pCFC 12 biases at year 297

GLODAP vs CESM control and New Steering Param (Exp018)

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pCFC 12 biases in sensitivity experiments 23, 24 and 25

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